GATE-2008 SYLLABUS-PAGE-2

IT - INFORMATION TECHNOLOGY

ENGINEERING MATHEMATICS

Mathematical Logic: Propositional Logic; First Order Logic.

Probability: Conditional Probability; Mean, Median, Mode and Standard Deviation; Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.

Set Theory & Algebra: Sets; Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra.

Combinatorics: Permutations; Combinations; Counting; Summation; generating functions; recurrence relations; asymptotics.

Graph Theory: Connectivity; spanning trees; Cut vertices & edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.

Linear Algebra: Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.

Numerical Methods: LU decomposition for systems of linear equations; numerical solutions of non linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson's rules.

Calculus: Limit, Continuity & differentiability, Mean value Theorems, Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.

FORMAL LANGUAGES AND AUTOMATA

Regular Languages: finite automata, regular expressions, regular grammar.

Context free languages: push down automata, context free grammars

COMPUTER HARDWARE

Digital Logic: Logic functions, minimization, design and synthesis of combinatorial and sequential circuits, number representation and computer arithmetic (fixed and floating point)

Computer organization: Machine instructions and addressing modes, ALU and data path, hardwired and microprogrammed control, memory interface, I/O interface (interrupt and DMA mode), serial communication interface, instruction pipelining, cache, main and secondary storage

SOFTWARE SYSTEMS

Data structures and Algorithms: the notion of abstract data types, stack, queue, list, set, string, tree, binary search tree, heap, graph, tree and graph traversals, connected components, spanning trees, shortest paths, hashing, sorting, searching, design techniques (greedy, dynamic, divide and conquer), asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, intractability

Programming Methodology: C programming, program control (iteration, recursion, functions), scope, binding, parameter passing, elementary concepts of object oriented programming

Operating Systems (in the context of Unix): classical concepts (concurrency, synchronization, deadlock), processes, threads and interprocess communication, CPU scheduling, memory management, file systems, I/O systems, protection and security

Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance.

Databases: relational model, database design, integrity constraints, normal forms, query languages (SQL), file structures (sequential, indexed), b-trees, transaction and concurrency control

Data Communication: data encoding and transmission, data link control, multiplexing, packet switching, LAN architecture, LAN systems (Ethernet, token ring), Network devices: switches, gateways, routers

Networks: ISO/OSI stack, sliding window protocols, routing protocols, TCP/UDP, application layer protocols & systems (http, smtp, dns, ftp), network security

Web technologies: three tier web based architecture; JSP, ASP, J2EE, .NET systems; html, XML

MA - MATHEMATICS

Linear Algebra: Finite dimensional vector spaces. Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton theorem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices. Finite dimensional inner product spaces, self-adjoint and Normal linear operators, spectral theorem, Quadratic forms.

Complex Analysis: Analytic functions, conformal mappings, bilinear transformations, complex integration: Cauchy's integral theorem and formula, Liouville's theorem, maximum modulus principle, Taylor and Laurent's series, residue theorem and applications for evaluating real integrals.

Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness. Lebesgue measure, measurable functions; Lebesgue integral, Fatou's lemma, dominated convergence theorem.

Ordinary Differential Equations: First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients, method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality, Sturm Liouville system, Greeen's functions.

Algebra: Normal subgroups and homomorphisms theorems, automorphisms. Group actions, sylow's theorems and their applications groups of order less than or equal to 20, Finite p-groups. Euclidean domains, Principal ideal domains and unique factorizations domains. Prime ideals and maximal ideals in commutative rings.

Functional Analysis: Banach spaces, Hahn-Banach theorems, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal sets, Riesz representation theorem, self-adjoint, unitary and normal linear operators on Hilbert Spaces.

Numerical Analysis: Numerical solution of algebraic and transcendental equations; bisection, secant method, Newton-Raphson method, fixed point iteration, interpolation: existence and error of polynomial interpolation, Lagrange, Newton, Hermite(osculatory)interpolations; numerical differentiation and integration, Trapezoidal and Simpson rules; Gaussian quadrature; (Gauss-Legendre and Gauss-Chebyshev), method of undetermined parameters, least square and orthonormal polynomial approximation; numerical solution of systems of linear equations: direct and iterative methods, (Jacobi Gauss-Seidel and SOR) with convergence; matrix eigenvalue problems: Jacobi and Given's methods, numerical solution of ordinary differential equations: initial value problems, Taylor series method, Runge-Kutta methods, predictor-corrector methods; convergence and stability.

Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems, Green's functions; solutions of Laplace, wave and diffusion equations in two variables Fourier series and transform methods of solutions of the above equations and applications to physical problems.

Mechanics: Forces in three dimensions, Poinsot central axis, virtual work, Lagrange's equations for holonomic systems, theory of small oscillations, Hamiltonian equations;

Topology: Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn's Lemma, Tietze extension theorem, metrization theorems, Tychonoff theorem on compactness of product spaces.

Probability and Statistics: Probability space, conditional probability, Bayes' theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments. Weak and strong law of large numbers, central limit theorem. Sampling distributions, UMVU estimators, sufficiency and consistency, maximum likelihood estimators. Testing of hypotheses, Neyman-Pearson tests, monotone likelihood ratio, likelihood ratio tests, standard parametric tests based on normal, X2 ,t, F-distributions. Linear regression and test for linearity of regression. Interval estimation.

Linear Programming: Linear programming problem and its formulation, convex sets their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods, infeasible and unbounded LPP's, alternate optima. Dual problem and duality theorems, dual simplex method and its application in post optimality analysis, interpretation of dual variables. Balanced and unbalanced transportation problems, unimodular property and u-v method for solving transportation problems. Hungarian method for solving assignment problems.

Calculus of Variations and Integral Equations: Variational problems with fixed boundaries; sufficient conditions for extremum, Linear integral equations of Fredholm and Volterra type, their iterative solutions. Fredholm alternative.

ME - MECHANICAL ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

Complex variables: Analytic functions, Cauchy's integral theorem, Taylor and Laurent series.

Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule, single and multi-step methods for differential equations.

APPLIED MECHANICS AND DESIGN

Engineering Mechanics: Equivalent force systems, free-body concepts, equations of equilibrium, trusses and frames, virtual work and minimum potential energy. Kinematics and dynamics of particles and rigid bodies, impulse and momentum (linear and angular), energy methods, central force motion.

Strength of Materials: Stress and strain, stress-strain relationship and elastic constants, Mohr's circle for plane stress and plane strain, shear force and bending moment diagrams, bending and shear stresses, deflection of beams, torsion of circular shafts, thin and thick cylinders, Euler's theory of columns, strain energy methods, thermal stresses.

Theory of Machines: Displacement, velocity and acceleration, analysis of plane mechanisms, dynamic analysis of slider-crank mechanism, planar cams and followers, gear tooth profiles, kinematics of gears, governors and flywheels, balancing of reciprocating and rotating masses.

Vibrations: Free and forced vibration of single degree freedom systems, effect of damping, vibration isolation, resonance, critical speed of rotors.

Design of Machine Elements: Design for static and dynamic loading, failure theories, fatigue strength; design of bolted, riveted and welded joints; design of shafts and keys; design of spur gears, rolling and sliding contact bearings; brakes and clutches; belt, rope and chain drives.

FLUID MECHANICS AND THERMAL SCIENCES

Fluid Mechanics: Fluid properties, fluid statics, manometry, buoyancy; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli's equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc.

Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer, black and grey surfaces, shape factors, network analysis; heat exchanger performance, LMTD and NTU methods.

Thermodynamics: Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; irreversibility and availability; behaviour of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion; Carnot, Rankine, Otto, Diesel, Brayton and vapour compression cycles.

Power Plant Engineering: Steam generators; steam power cycles; steam turbines; impulse and reaction principles, velocity diagrams, pressure and velocity compounding; reheating and reheat factor; condensers and feed heaters.

I.C. Engines: Requirements and suitability of fuels in IC engines, fuel ratings, fuel-air mixture requirements; normal combustion in SI and CI engines; engine performance calculations.

Refrigeration and air-conditioning: Refrigerant compressors, expansion devices, condensers and evaporators; properties of moist air, psychrometric chart, basic psychometric processes.

Turbomachinery: Components of gas turbines; compression processes, centrifugal and axial flow compressors; axial flow turbines, elementary theory; hydraulic turbines; Euler-turbine equation; specific speed, Pelton-wheel, Francis and Kaplan turbines; centrifugal pumps.

MANUFACTURING AND INDUSTRIAL ENGINEERING

Engineering Materials: Structure and properties of engineering materials and their applications, heat treatment.

Metal Casting: Casting processes (expendable and non-expendable) -pattern, moulds and cores, heating and pouring, solidification and cooling, gating design, design considerations, defects.

Forming Processes: Stress-strain diagrams for ductile and brittle material, Plastic deformation and yield criteria, fundamentals of hot and cold working processes, Bulk metal forming processes (forging, rolling, extrusion, drawing), sheet metal working processes (punching, blanking, bending, deep drawing, coining, spinning, load estimation using homogeneous deformation methods, defects). processing of powder metals- atomization, compaction, sintering, secondary and finishing operations. forming and shaping of plastics- extrusion, injection moulding.

Joining Processes: Physics of welding, fusion and non-fusion welding processes, brazing and soldering, adhesive bonding, design considerations in welding, weld quality defects.

Machining and Machine Tool Operations: Mechanics of machining, single and multi-point cutting tools, tool geometry and materials, tool life and wear, cutting fluids, machinability, economics of machining, non-traditional machining processes.

Metrology and Inspection: Limits, fits and tolerances, linear and angular measurements, comparators, gauge design, interferometry, form and finish measurement, measurement of screw threads, alignment and testing methods.

Tool Engineering: Principles of work holding, design of jigs and fixtures.

Computer Integrated Manufacturing: Basic concepts of CAD, CAM and their integration tools.

Manufacturing Analysis: Part-print analysis, tolerance analysis in manufacturing and assembly, time and cost analysis.

Work-Study: Method study, work measurement, time study, work sampling, job evaluation, merit rating.

Production Planning and Control: Forecasting models, aggregate production planning, master scheduling, materials requirements planning.

Inventory Control: Deterministic and probabilistic models, safety stock inventory control systems.

Operations Research: Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM


MN - MINING ENGINEERING

ENGINEERING MATHEMATICS:

Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green's theorems.

Diferential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs - Laplace, heat and wave equations.

Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.

Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson's rule; single and multi-step methods for differential equations.

MINING ENGINEERING

Mechanics: Equivalent force systems, equations of equilibrium, two dimensional frames and trusses, free body diagrams, friction forces, particle kinematics and dynamics.

Mine Development, Geomechanics and Strata Control: Drivages for underground mine development, drilling methods and machines, explosives, blasting devices and practices, shaft sinking. Physico-mechanical properties of rocks, rock mass classification, ground control instrumentation and stress measurement techniques, theories of rock failure, ground vibrations, stress distribution around mine openings, subsidence, design of supports in roadways and workings, stability of open pits, slopes.

Mining Methods and Machinery: Surface mining - layout, development, loading, transportation and mechanization, continuous surface mining systems. Underground coal mining - bord and pillar system, longwall mining, thick seam mining methods. Underground metal mining: different stoping methods, stope mechanization, ore handling systems, mine filling. Generation and transmission of mechanical, hydraulic, and pneumatic power. Materials handling - haulages, conveyors, ropeways, face and development machinery, hoisting systems, and pumps.

Ventilation, Underground Hazards and Surface Environment: Underground atmosphere, heat load sources and thermal environment, air cooling, mechanics of air flow distribution, natural and mechanical ventilation, mine fans and their usage, auxiliary ventilation. Subsurface hazards from fires, explosions, gases, dust, and inundation, rescue apparatus and practices, safety in mines, accident analysis, noise, mine lighting. Air and water pollution: causes, dispersion, quality standards, and control.

Surveying, Mine Planning and Systems Engineering: Fundamentals of engineering surveying, Levels and levelling, Theodolite, tacheometry, triangulation, contouring, errors and adjustments, correlation, underground surveying, curves, photogrammetry, field astronomy, GPS fundamentals. Principles of planning - Sampling methods and practices, reserve estimation techniques, basics of geostatistics, optimization of facility location, cash flow concepts and mine valuation, open pit design. Work study, concepts of reliability, reliability of series and parallel systems. Linear programming, transportation and assignment problems, queueing, network analysis, inventory control.

MT - METALLURGICAL ENGINEERING

ENGINEERING MATHEMATICS:

Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green's theorems.

Diferential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs - Laplace, heat and wave equations.

Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.

Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson's rule; single and multi-step methods for differential equations.

METALLURGICAL ENGINEERING

Thermodynamics and Rate Processes: Laws of thermodynamics, activity, equilibrium constant, applications to metallurgical systems, solutions, phase equilibria, basic kinetic laws, order of reactions, rate constants and rate limiting steps principles of electro chemistry, aqueous, corrosion and protection of metals, oxidation and high temperature corrosion - characterization and control; momentum transfer - concepts of viscosity, shell balances, Bernoulli's equation; heat transfer - conduction, convection and heat transfer coefficient relations, radiation, mass transfer - diffusion and Fick's laws.

Extractive Metallurgy: Flotation, gravity and other methods of mineral processing; agglomeration, pyro-hydro-and electro-metallurgical processes; material and energy balances; principles and processes for the extraction of non-ferrous metals - aluminium, copper, zinc, lead, magnesium, nickel, titanium and other rare metals; iron and steel making - principles, blast furnace, direct reduction processes, primary and secondary steel making, deoxidation and inclusion in steel; ingot and continuous casting; stainless steel making, design of furnaces; fuels and refractories.

Physical Metallurgy: Crystal structure and bonding characteristics of metals, alloys, ceramics and polymers; solid solutions; solidification; phase transformation and binary phase diagrams; principles of heat treatment of steels, aluminum alloys and cast irons; recovery, recrystallization and grain growth; industrially important ferrous and non-ferrous alloys; elements of X-ray and electron diffraction; principles of scanning and transmission electron microscopy; elements of ceramics, composites and electronic materials; electronic basis of thermal, optical, electrical and magnetic properties of materials.

Mechanical Metallurgy: Elements of elasticity and plasticity; defects in crystals; elements of dislocation theory - types of dislocations, slip and twinning, stress fields of dislocations, dislocation interactions and reactions, methods of seeing dislocations; strengthening mechanisms; tensile, fatigue and creep behaviour; superplasticity; fracture - Griffith theory, ductile to brittle transition, fracture toughness; failure analysis; mechanical testing - tension, compression, torsion, hardness, impact, creep, fatigue, fracture toughness and formability tests.

Manufacturing Processes: Metal casting - patterns, moulds, melting, gating, feeding and casting processes, defects and castings, hot and cold working of metals; Metal forming - fundamentals of metal forming, rolling wire drawing, extrusion, forming, sheet metal forming processes, defects in forming; Metal joining - soldering, brazing and welding, common welding processes, welding metallurgy, problems associated with welding of steels and aluminium alloys, defects in welding, powder metallurgy; NDT methods - ultrasonic, radiography, eddy current, acoustic emission and magnetic.

PH - PHYSICS

Mathematical Physics: Linear vector space, matrices; vector calculus; linear differential equations; elements of complex analysis; Laplace transforms, Fourier analysis, elementary ideas about tensors.

Classical Mechanics: Conservation laws; central forces; collisions and scattering in laboratory and centre of mass reference frames; mechanics of system of particles; rigid body dynamics; moment of inertia tensor; noninertial frames and pseudo forces; variational principle; Lagrange's and Hamilton's formalisms; equation of motion, cyclic coordinates, Poisson bracket; periodic motion, small oscillations, normal modes; wave equation and wave propagation; special theory of relativity - Lorentz transformations, relativistic kinematics, mass-energy equivalence.

Electromagnetic Theory: Laplace and Poisson equations; conductors and dielectrics; boundary value problems; Ampere's and Biot-Savart's laws; Faraday's law; Maxwell's equations; scalar and vector potentials; Coulomb and Lorentz gauges; boundary conditions at interfaces; electromagnetic waves; interference, diffraction and polarization; radiation from moving charges.

Quantum Mechanics: Physical basis of quantum mechanics; uncertainty principle; Schrodinger equation; one and three dimensional potential problems; Particle in a box, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and spin; addition of angular momentum; time independent perturbation theory; elementary scattering theory.

Atomic and Molecular Physics: Spectra of one-and many-electron atoms; LS and jj coupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; X-ray spectra; rotational and vibrational spectra of diatomic molecules; electronic transition in diatomic molecules, Franck-Condon principle; Raman effect; NMR and ESR; lasers.

Thermodynamics and Statistical Physics: Laws of thermodynamics; macrostates, phase space; probability ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body radiation and Planck's distribution law; Bose-Einstein condensation; first and second order phase transitions, critical point.

Solid State Physics: Elements of crystallography; diffraction methods for structure determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors and insulators; transport properties; optical, dielectric and magnetic properties of solids; elements of superconductivity.

Nuclear and Particle Physics: Rutheford scattering; basic properties of nuclei; radioactive decay; nuclear forces; two nucleon problem; nuclear reactions; conservation laws; fission and fusion; nuclear models; particle accelerators, detectors; elementary particles; photons, baryons, mesons and leptons; Quark model.

Electronics: Network analysis; semiconductor devices; bipolar transistors; FETs; power supplies, amplifier, oscillators; operational amplifiers; elements of digital electronics; logic circuits.

PI - PRODUCTION AND INDUSTRIAL ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

Complex variables: Analytic functions, Cauchy's integral theorem, Taylor and Laurent series.

Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule, single and multi-step methods for differential equations.

GENERAL ENGINEERING:

Engineering Materials: Structure and properties of engineering materials and their applications; effect of strain, strain rate and temperature on mechanical properties of metals and alloys; heat treatment of metals and alloys.

Applied Mechanics: Engineering mechanics - equivalent force systems, free body concepts, equations of equilibrium, virtual work and minimum potential energy; strength of materials- stress, strain and their relationship, Mohr's circle, deflection of beams, bending and shear stress, Euler's theory of columns.

Theory of Machines and Design: Analysis of planar mechanisms, plane cams and followers; governers and fly wheels; design of elements-failure theories; design of bolted, riveted and welded joints; design of shafts, keys, belt drives, brakes and clutches.

Thermal Engineering: Fluid machines - fluid statics, Bernoulli's equation, flow through pipes, equations of continuity and momentum; Thermodynamics - zeroth, First and Second laws of thermodynamics, thermodynamic system and processes, calculation of work and heat for systems and control volumes; Heat transfer - fundamentals of conduction, convection and radiation.

PRODUCTION ENGINEERING

Metal Casting: Casting processes; patterns-materials; allowances; moulds and cores - materials, making and testing; melting and founding of cast iron, steels and nonferrous metals and alloys; solidification; design of casting, gating and risering; casting defects and inspection.

Metal working: Stress-strain in elastic and plastic deformation; deformation mechanisms; hot and cold working-forging, rolling, extrusion, wire and tube drawing; sheet metal working; analysis of rolling, forging, extrusion and wire /rod drawing; metal working defects, high energy rate forming processes-explosive, magnetic, electro and electrohydraulic.

Metal Joining Processes: Welding processes - gas shielded metal arc, TIG, MIG, submerged arc, electroslag, thermit, resistance, pressure and forge welding; thermal cutting; other joining processes - soldering, brazing, braze welding; welding codes, welding symbols, design of welded joints, defects and inspection; introduction to modern welding processes - friction, ultrasonic, explosive, electron beam, laser and plasma.

Machining and Machine Tool Operations: Machining processes-turning, drilling, boring, milling, shaping, planing, sawing, gear cutting, thread production, broaching, grinding, lapping, honing super finishing; mechanics of cutting- Merchant's analysis, geometry of cutting tools, cutting forces, power requirements; selection of process parameters; tool materials, tool wear and tool life, cutting fluids, machinability; nontraditional machining processes and hybrid processes- EDM, CHM, ECM, USM, LBM, EBM, AJM, PAM AND WJM; economics of machining.

Metrology and Inspection: Limits and fits, linear and angular measurements by mechanical and optical methods, comparators; design of limit gauges; interferometry; measurement of straightness, flatness, roundness, squareness and symmetry; surface finish measurement; inspection of screw threads and gears; alignment testing.

Powder Metallurgy and Processing of Plastics: Production of powders, compaction, sintering; Polymers and composites; injection, compression and blow molding, extrusion, calendaring and thermoforming; molding of composites.

Tool Engineering: Work-holding-location and clamping; principles and methods; design of jigs and fixtures; design of press working tools, forging dies.

Manufacturing Analysis: Sources of errors in manufacturing; process capability; part-print analysis; tolerance analysis in manufacturing and assembly; process planning; parameter selection and comparison of production alternatives; time and cost analysis; Issues in choosing manufacturing technologies and strategies.

Computer Integrated Manufacturing: Basic concepts of CAD, CAM, CAPP, group technology, NC, CNC, DNC, FMS, Robotics and CIM.

INDUSTRIAL ENGINEERING

Product Design and Development: Principles of good product design, component and tolerance design; efficiency, quality and cost considerations; product life cycle; standardization, simplification, diversification, value analysis, concurrent engineering.

Engineering Economy and Costing: Financial statements; elementary cost accounting, methods of depreciation; break-even analysis, techniques for evaluation of capital investments.

Work System Design: Taylor's scientific management, Gilbreths's contributions; productivity concepts and measurements; method study, micro-motion study, principles of motion economy; human factors engineering, ergonomics; work measurement - time study, PMTS, work sampling; job evaluation, merit rating, wage administration, incentive systems; business process reengineering.

Logistics and Facility Design: Facility location factors, evaluation of alternatives, types of plant layout, evaluation; computer aided layout; assembly line balancing; material handling systems; supply chain management.

Production Planning and Inventory Control: Inventory Function costs, classifications - deterministic and probabilistic models; quantity discount; safety stock; inventory control system; Forecasting techniques - causal and time series models, moving average, exponential smoothing; trend and seasonality; aggregate production planning; master scheduling; bill of materials and material requirement planning; order control and flow control, routing, scheduling and priority dispatching; JIT; Kanban PULL systems; bottleneck scheduling and theory of constraints.

Operation Research: Linear programming - problem formulation, simplex method, duality and sensitivity analysis; transportation; assignment; network flow models, constrained optimization and Lagrange multipliers; simple queuing models; dynamic programming; simulation; PERT and CPM, time-cost trade-off, resource leveling.

Quality Control: Taguchi method; design of experiments; quality costs, statistical quality assurance, process control charts, acceptance sampling, zero defects; quality circles, total quality management.

Reliability and Maintenance: Reliability, availability and maintainability; probabilistic failure and repair times; system reliability; preventive maintenance and replacement, TPM.

Management Information System: Value of information; information storage and retrieval system - database and data structures; interactive systems; knowledge based systems.

Intellectual Property System: Definition of intellectual property, importance of IPR; TRIPS, and its implications, WIPO and Global IP structure, and IPS in India; patent, copyright, industrial design and trademark; meanings, rules and procedures, terms, infringements and remedies.

PY - PHARMACEUTICAL SCIENCES

Natural Products: Pharmacognosy & Phytochemistry - Chemistry, tests, isolation, characterization and estimation of phytopharmaceuticals belonging to the group of Alkaloids, Glycosides, Terpenoids, Steroids, Bioflavanoids, Purines, Guggul lipids. Pharmacognosy of crude drugs which contain the above constituents. Standardisation of raw materials and herbal products. WHO guide lines. Quantitative microscopy including modern techniques used for evaluation. Biotechnological principles and techniques for plant development Tissue culture.

Pharmacology: General pharmacological principles including Toxicology. Drug interaction. Pharmacology of drugs acting on Central nervous system, Cardiovascular system, Autonomic nervous system, Gastro intestinal system and Respiratory system. Pharmacology of Autocoids, Hormones, Chemotherapeutic agents including anticancer drugs. Bioassays. Immuno Pharmacology.

Medicinal Chemistry: Structure, nomenclature, classification, synthesis, SAR and metabolism of the following category of drugs which are official in Indian Pharmacopoeia and British Pharmacopoeia Hypnotics and Sedatives, Analgesics, NSAIDS, Neuroleptics, Antidepressants, Anxiolytics, Anticonvulsants, Antihistaminics, Local anaesthetics, Cardio Vascular drugs - Antianginal agents Vasodilators, Adrenergic & cholinergic drugs, Cardiotonic agents, Diuretics, Antihypertensive drugs, Hypoglycemic agents, Antilipedmic agents, Coagulants, Anticoagulants, Antiplatelet agents. Chemotherapeutic agents - Antibiotics, Antibacterials, Sulphadrugs. Antiproliozoal drugs, Antiviral, Antitubercular, Antimalarial, Anticancer, Antiamoebic drugs. Diagnostic agents. Preparation and storage and uses of official Radiopharmaceuticals. Vitamins and Hormones.

Pharmaceutics: Development, manufacturing standards, labeling, packing as per the pharmacopoeal requirements, Storage of different dosage forms and new drug delivery systems. Biopharmaceutics and Pharmacokinetics and their importance in formulation. Formulation and preparation of cosmetics - lipstick, shampoo, creams, nail preparations and dentifrices. Pharmaceutical calculations.

Pharmaceutical Jurisprudence: Legal aspects of manufacture, storage, sale of drugs. D and C act and rules. Pharmacy act.

Pharmaceutical Analysis: Principles, instrumentation and applications of the following. Absorption spectroscopy (UV, visible & IR), Fluorimetry, Flame photometry, Potentiometry, Conductometry and Plarography. Pharmacopoeial assays. Principles of NMR, ESR, Mass spectroscopy, X-ray diffraction analysis and different chromatographic methods.

Biochemistry and Clinical Pharmacy: Biochemical role of hormones, Vitamins, Enzymes, Nucleic acids. Bioenergetics. General principles of immunology. Immunological techniques. Adverse drug interaction.

Microbiology: Principles and methods of microbiological assays of the Pharmacopoeia. Methods of preparation of official sera and vaccines. Serological and diagnostic tests. Applications of microorganisms in Bio Conversions and in Pharmaceutical industry.

TF - TEXTILE ENGINEERING AND FIBRE SCIENCE

ENGINEERING MATHEMATICS:

Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green's theorems.

Diferential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs - Laplace, heat and wave equations.

Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.

Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson's rule; single and multi-step methods for differential equations.

TEXTILE ENGINEERING & FIBRE SCIENCE

Textile Fibres: Classification of textile fibres according to their nature and origin; general characteristics of textile fibres-their chemical and physical structures and their properties; essential characteristics of fibre forming polymers; uses of natural and man-made fibres; physical and chemical methods of fibre and blend identification and blend analysis.

Melt Spinning processes with special reference to polyamide and polyester fibres; wet and dry spinning of viscose and acrylic fibres; post spinning operations-drawing, heat setting, texturing- false twist and air-jet, tow-to-top conversion. Methods of investigating fibre structure e.g. X-ray diffraction, birefringence, optical and electron microscopy, I.R. absorption, thermal methods; structure and morphology and principal natural and man-made fibres, mechanical properties of fibres, moisture sorption in fibres; fibre structure and property correlation.

Textile Testing: Sampling techniques, sample size and sampling errors; measurement of fibre length, fineness, crimp, strength and reflectance; measurement of cotton fibre maturity ad trash content; HVI and AFIS for fibre testing. Measurement of yarn count, twist and hairiness; tensile testing of fibres, yarn and fabrics; evenness testing of slivers, rovings and yarns; testing equipment for measurement test methods of fabric properties like thickness, compressibility, air permeability, drape, crease recovery, tear strength bursting strength and abrasion resistance. Correlation analysis, significance tests and analysis of variance; frequency distributions and control charts.

Yarn Manufacture and Yarn Structure: Modern methods of opening, cleaning and blending of fibrous materials; the technology of carding with particular reference to modern developments; causes of irregularity introduced by drafting, the development of modern drafting systems; principles and techniques of preparing material for combing; recent development in combers; functions and synchronization of various mechanisms concerned with roving production; forces acting on yarn and traveller, ring and traveller designs; causes of end breakages; properties of doubles yarns; new methods of yarn production such as rotor spinning, air jet spinning and friction spinning.

Yarn diameter; specific volume, packing coefficient; twist-strength relationship; fibre orientation in yarn; fibre migration.

Fabric Manufacture and Fabric Structure: Principles of cheese and cone winding processes and machines; random and precision winding; package faults and their remedies; yarn clearers and tensioners; different systems of yarn splicing; features of modern cone winding machines; different types of warping creels; features of modern beam and sectional warping machines; different sizing systems, sizing of spun and filament yarns, modern sizing machines; principles of pirn winding processes and machines; primary and secondary motions of loom, effect of their settings and timings on fabric formation, fabric appearance and weaving performance; dobby and jacquard shedding; mechanics of weft insertion with shuttle; warp and weft stop motions, warp protection, weft replenishment; functional principles of weft insertion systems of shuttleless weaving machines, principles of multiphase and circular looms. Principles of weft and warp knitting; basic weft and warp knitted structures; classification, production and areas of application of nonwoven fabrics.

Basic woven fabric constructions and their derivatives; crepe, cord, terry, gauze, lino and double cloth constructions.

Peirce's equations for fabric geometry; thickness, cover and maximum sett of woven fabrics

Textile Chemical Processing: Preparatory processes for natural-and and their blends; mercerization of cotton; machines for yarn and fabric mercerization.

Dyeing and printing of natural- and synthetic- fibre fabrics and their blends with different dye classes; dyeing and printing machines; styles of printing; fastness properties of dyed and printed textile materials.

Finishing of textile materials, wash and wear, durable press, soil release, water repellent, flame retardant and antistatic finishes; shrink-resistance finish for wool; heat setting of synthetic-fibre fabrics, finishing machines; energy efficient processes; pollution control.

XE - ENGINERING SCIENCES

The syllabi of the sections of this paper are as follows:

SECTION A. ENGINEERING MATHEMATICS (Compulsory)

Linear Algebra : Determinates, algebra of matrices, rank, inverse, system of linear equations, symmetric, skew-symmetric and orthogonal matrices. Hermitian, skew-hermitian and unitary matrices. eigenvalues and eigenvectors, diagonalisation of matrices, Cayley-Hamiltonian, quadratic forms.

Calculus : Functions of single variables, limit, continuity and differentiability, Mean value theorems, Intermediate forms and L'Hospital rule, Maxima and minima, Taylor's series, Fundamental and mean value-theorems of integral calculus. Evaluation of definite and improper integrals, Beta and Gamma functions, Functions of two variables, limit, continuity, partial derivatives, Euler's theorem for homogeneous functions, total derivatives, maxima and minima, Lagrange method of multipliers, double and triple integrals and their applications, sequence and series, tests for convergence, power series, Fourier Series, Fourier integrals.

Complex variable: Analytic functions, Cauchy's integral theorem and integral formula without proof. Taylor's and Laurent' series, Residue theorem (without proof) with application to the evaluation of real integarls.

Vector Calculus: Gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green's theorems (without proofs) with applications.

Ordinary Differential Equations: First order equation (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of paramaters, Cauchy's and Euler's equations, initial and boundary value problems, power series solutions, Legendre polynomials and Bessel's functions of the first kind.

Partial Differential Equations: Variables separable method, solutions of one dimensional heat, wave and Laplace equations.

Probability and Statistics: Definitions of probability and simple theorems, conditional probability, mean, mode and standard deviation, random variables, discrete and continuous distributions, Poisson, normal and Binomial distribution, correlation and regression

Numerical Methods: L-U decomposition for systems of linear equations,Newton-Raphson method, numerical integration(trapezoidal and Simpson's rule), numerical methods for first order differential equation (Euler method)

SECTION B. COMPUTATIONAL SCIENCE

Numerical Methods: Truncation errors, round off errors and their propagation; Interpolation; Lagrange, Newton's forward, backward and divided difference formulas, least square curve fitting, solution of non-linear equations of one variables using bisection, false position, secant and Newton Raphson methods; Rate of convergence of these methods, general iterative methods. Simple and multiple roots of polynomials. Solutions of system of linear algebraic equations using Gauss elimination methods, Jacobi and Gauss-Seidel iterative methods and their rate of convergence; ill conditioned and well conditioned system. eigen values and eigen vectors using power methods. Numerical integration using trapezoidal, Simpson's rule and other quadrature formulas. Numerical Differentiation. Solution of boundary value problems. Solution of initial value problems of ordinary differential equations using Euler's method, predictor corrector and Runge Kutta method.

Programming : Elementary concepts and terminology of a computer system and system software, Fortran77 and C programming.

Fortran : Program organization, arithmetic statements, transfer of control, Do loops, subscripted variables, functions and subroutines.

C language : Basic data types and declarations, flow of control- iterative statement, conditional statement, unconditional branching, arrays, functions and procedures.

SECTION C. ELECTRICAL SCIENCES

Electric Circuits: Ideal voltage and current sources; RLC circuits, steady state and transient analysis of DC circuits, network theorems; alternating currents and voltages, single-phase AC circuits, resonance; three-phase circuits.

Magnetic circuits: Mmf and flux, and their relationship with voltage and current; transformer, equivalent circuit of a practical transformer, three-phase transformer connections.

Electrical machines: Principle of operation, characteristics, efficiency and regulation of DC and synchronous machines; equivalent circuit and performance of three-phase and single-phase induction motors.

Electronic Circuits: Characteristics of p-n junction diodes, zener diodes, bipolar junction transistors (BJT) and junction field effect transistors (JFET); MOSFET's structure, characteristics, and operations; rectifiers, filters, and regulated power supplies; biasing circuits, different configurations of transistor amplifiers, class A, B and C of power amplifiers; linear applications of operational amplifiers; oscillators; tuned and phase shift types.

Digital circuits: Number systems, Boolean algebra; logic gates, combinational circuits, flip-flops (RS, JK, D and T) counters.

Measuring instruments: Moving coil, moving iron, and dynamometer type instruments; shunts, instrument transformers, cathode ray oscilloscopes; D/A and A/D converters.

SECTION D. FLUID MECHANICS

Fluid Properties: Relation between stress and strain rate for Newtonian fluids

Hydrostatics, buoyancy, manometry

Concept of local and convective accelerations; control volume analysis for mass, momentum and energy conservation.

Differential equations of continuity and momentum (Euler's equation of motion); concept of fluid rotation, stream function, potential function; Bernoulli's equation and its applications.

Qualitative ideas of boundary layers and its separation; streamlined and bluff bodies; drag and lift forces.

Fully-developed pipe flow; laminar and turbulent flows; friction factor; Darcy Weisbach relation; Moody's friction chart; losses in pipe fittings; flow measurements using venturimeter and orifice plates.

Dimensional analysis; similitude and concept of dynamic similarity; importance of dimensionless numbers in model studies.

SECTION E. MATERIALS SCIENCE

Atomic structure and bonding in materials: metals, ceramics and polymers.

Structure of materials: Crystal systems, unit cells and space lattice; determination of structures of simple crystals by X-ray diffraction; Miller indices for planes and directions. Packing geometry in metallic, ionic and covalent solids.

Concept of amorphous, single and polycrystalline structures and their effects on properties of materials.

Imperfections in crystalline solids and their role in influencing various properties.

Fick´s laws of diffusion and applications of diffusion in sintering, doping of semiconductors and surface hardening of metals.

Alloys: solid solution and solubility limit. Binary phase diagram, intermediate phases and intermetallic compounds; iron-iron carbide phase diagram. Phase transformation in steels. Cold and hot working of metals, recovery, recrystallization and grain growth.

Properties and applications of ferrous and nonferrous alloys.

Structure, properties, processing and applications of traditional and advanced ceramics.

Polymers: classification, polymerization, structure and properties, additives for polymer products, processing and application.

Composites: properties and application of various composites.

Corrosion and environmental degradation of materials (metals, ceramics and polymers).

Mechanical properties of materials: Stress-strain diagrams of metallic, ceramic and polymeric materials, modulus of elasticity, yield strength, plastic deformation and toughness, tensile strength and elongation at break; viscoelasticity, hardness, impact strength. ductile and brittle fracture. creep and fatigue properties of materials.

Heat capacity, thermal conductivity, thermal expansion of materials.

Concept of energy band diagram for materials; conductors, semiconductors and insulators in terms of energy bands. Electrical conductivity, effect of temperature on conductivity in materials, intrinsic and extrinsic semiconductors, dielectric properties of materials.

Refraction, reflection, absorption and transmission of electromagnetic radiation in solids.

Origin of magnetism in metallic and ceramic materials, paramagnetism, diamagnetism, antiferromagnetism, ferromagnetism, ferrimagnetism in materials and magnetic hysteresis.

Advanced materials: Smart materials exhibiting ferroelectric, piezoelectric, optoelectronic, semiconducting behaviour; lasers and optical fibers; photoconductivity and superconductivity in materials.

SECTION F. SOLID MECHANICS

Equivalent force systems; free-body diagrams; equilibrium equations; analysis of determinate and indeterminate trusses and frames; friction.

Simple relative motion of particles; force as function of position, time and speed; force acting on a body in motion; laws of motion; law of conservation of energy; law of conservation of momentum

Stresses and strains; principal stresses and strains; Mohr's circle; generalized Hooke's Law; equilibrium equations; compatibility conditions; yield criteria.

Axial, shear and bending moment diagrams; axial, shear and bending stresses; deflection (for symmetric bending); torsion in circular shafts; thin cylinders; energy methods (Castigliano's Theorems); Euler buckling.

SECTION G. THERMODYNAMICS

Basic Concepts: Continuum, macroscopic approach, thermodynamic system (closed and open or control volume); thermodynamic properties and equilibrium; state of a system, state diagram, path and process; different modes of work; Zeroth law of thermodynamics; concept of temperature; heat.

First Law of Thermodynamics: Energy, enthalpy, specific heats, first law applied to systems and control volumes, steady and unsteady flow analysis.

Second Law of Thermodynamics: Kelvin-Planck and Clausius statements, reversible and irreversible processes, Carnot theorems, thermodynamic temperature scale, Clausius inequality and concept of entropy, principle of increase of entropy; availability and irreversibility.

Properties of Pure Substances: Thermodynamic properties of pure substances in solid, liquid and vapour phases, P-V-T behaviour of simple compressible substances, phase rule, thermodynamic property tables and charts, ideal and real gases, equations of state, compressibility chart.

Thermodynamic Relations: T-ds relations, Maxwell equations, Joule-Thomson coefficient, coefficient of volume expansion, adiabatic and isothermal compressibilities, Clapeyron equation.

Ideal Gas Mixtures: Dalton's and Amagat's laws, calculations of properties, air-water vapour mixtures.